{"title":"A composition method for neat formulas of chromatic symmetric functions","authors":"David G.L. Wang , James Z.F. Zhou","doi":"10.1016/j.aam.2025.102886","DOIUrl":"10.1016/j.aam.2025.102886","url":null,"abstract":"<div><div>We develop a composition method to unearth positive <span><math><msub><mrow><mi>e</mi></mrow><mrow><mi>I</mi></mrow></msub></math></span>-expansions of chromatic symmetric functions <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>G</mi></mrow></msub></math></span>, where the subscript <em>I</em> stands for compositions rather than integer partitions. Using this method, we derive positive and neat <span><math><msub><mrow><mi>e</mi></mrow><mrow><mi>I</mi></mrow></msub></math></span>-expansions for the chromatic symmetric functions of tadpoles, barbells and generalized bulls, and establish the <em>e</em>-positivity of hats. We also obtain a compact ribbon Schur analog for the chromatic symmetric function of cycles.</div></div>","PeriodicalId":50877,"journal":{"name":"Advances in Applied Mathematics","volume":"167 ","pages":"Article 102886"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Generating Mandelbrot and Julia sets using PV iterative technique","authors":"Pragati Gautam , Vineet","doi":"10.1016/j.chaos.2025.116346","DOIUrl":"10.1016/j.chaos.2025.116346","url":null,"abstract":"<div><div>In this study, we utilize the PV iteration method to generate Mandelbrot and Julia sets for the function <span><math><mrow><mi>G</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><msup><mrow><mi>z</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>+</mo><mi>c</mi></mrow></math></span>. We establish escape criterion conditions for the PV iteration and provide a variety of graphical examples for different parameter settings. We also compare the graphs with those generated by other well-known iterations, such as the Picard-Mann and M iterations. Furthermore, we investigate the dependency between the iteration’s parameters and three numerical measures: the average escape time (AET), the non-escaping area index (NAI), and the fractal generation time. A comparative analysis is conducted with the renowned Mann, Picard-Mann, and M iteration methods. The results demonstrate that the fractals generated by the PV iteration exhibit distinct characteristics compared to those generated by other iterations, with non-linear dependencies that vary between different methods. These findings highlight the unique properties and potential applications of PV iteration in fractal generation.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116346"},"PeriodicalIF":5.3,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xinxin Qie, Jie Zang, Shenquan Liu, Andrey L Shilnikov
{"title":"Synaptic delays shape dynamics and function in multimodal neural motifs.","authors":"Xinxin Qie, Jie Zang, Shenquan Liu, Andrey L Shilnikov","doi":"10.1063/5.0233640","DOIUrl":"https://doi.org/10.1063/5.0233640","url":null,"abstract":"<p><p>In neuroscience, delayed synaptic activity plays a pivotal and pervasive role in influencing synchronization, oscillation, and information-processing properties of neural networks. In small rhythm-generating networks, such as central pattern generators (CPGs), time-delays may regulate and determine the stability and variability of rhythmic activity, enabling organisms to adapt to environmental changes, and coordinate diverse locomotion patterns in both function and dysfunction. Here, we examine the dynamics of a three-cell CPG model in which time-delays are introduced into reciprocally inhibitory synapses between constituent neurons. We employ computational analysis to investigate the multiplicity and robustness of various rhythms observed in such multi-modal neural networks. Our approach involves deriving exhaustive two-dimensional Poincaré return maps for phase-lags between constituent neurons, where stable fixed points and invariant curves correspond to various phase-locked and phase-slipping/jitter rhythms. These rhythms emerge and disappear through various local (saddle-node, torus) and non-local (homoclinic) bifurcations, highlighting the multi-functionality (modality) observed in such small neural networks with fast inhibitory synapses.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143763028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Machine-learning potential energy surfaces implications in photodissociation process.","authors":"Joaquin de la Cerda, Johan F Triana","doi":"10.1063/5.0249690","DOIUrl":"https://doi.org/10.1063/5.0249690","url":null,"abstract":"<p><p>Multi-state quantum molecular dynamics is one of the most accurate methodologies for predicting rates and yields of different chemical reactions. However, the generation of potential energy surfaces (PES), transition dipoles, and non-adiabatic couplings from ab initio calculations become a challenge, especially because of the exponential growth of computational cost as the number of electrons and molecular modes increases. Thus, machine learning (ML) emerges as a novel technique to compute molecular properties using fewer resources. Yet, the validity of ML methodologies continues in constant development, particularly for high-energy regions where conventional ab initio sampling is reduced. We test the accuracy of the potential energy surfaces interpolated with machine learning (ML) techniques in the solution of the time-dependent Schrödinger equation for the conventional IR+UV bond-breaking process of semi-heavy water. We perform a statistical analysis of the differences in expectation values and dissociation probabilities, which depend on the number of ab initio points selected to generate the machine learning potential energy surface (ML-PES). The energy differences of the electronic excited state modify population transfer from the ground state by driving with a UV laser pulse. We consider as the exact solution the photodynamics implemented with analytical expressions of the electronic ground X~1A1 and excited A~1B1 states. The results of the mean bond distance and dissociation probabilities suggest that ML-PES is suitable for dynamics calculations around the Franck-Condon region, and that standard interpolation methods are more efficient for multistate dynamics that involve dissociative and repulsive energy regions of the electronic states. Our work contributes to the continued inclusion of ML tools in molecular dynamics to obtain accurate predictions of dissociation yields with fewer computational resources and non-written rules to follow in multi-state dynamics calculations.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 4","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143762456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Interaction topology optimization by adjustment of edge weights to improve the consensus convergence and prolong the sampling period for a multi-agent system","authors":"Tongyou Xu , Ying-Ying Tan , Shanshan Gao , Xuejuan Zhan","doi":"10.1016/j.amc.2025.129428","DOIUrl":"10.1016/j.amc.2025.129428","url":null,"abstract":"<div><div>The second smallest eigenvalue and the largest eigenvalue of the Laplacian matrix of a simple undirected connected graph <em>G</em> are called the algebraic connectivity <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and the Laplacian spectral radius <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span>, respectively. For a first-order periodically sampled consensus protocol multi-agent system (MAS), whose interaction topology can be modeled as a graph <em>G</em>, a larger <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> results in a faster consensus convergence rate, while a smaller <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> contributes to a longer sampling period of the system. Adjusting the weights of the edges is an efficient approach to optimize the interaction topology of a MAS, which improves the consensus convergence rate and prolongs the sampling period. If <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> increases, then the weight of one edge <span><math><mo>{</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>}</mo></math></span> increases, i.e., the increment <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo>></mo><mn>0</mn></math></span>, and the entries of its eigenvector with respect to <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> are not equal. If <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> decreases, then the weight of one edge <span><math><mo>{</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>,</mo><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>}</mo></math></span> decreases, i.e., the increment <span><math><msub><mrow><mi>δ</mi></mrow><mrow><mi>s</mi><mi>t</mi></mrow></msub><mo><</mo><mn>0</mn></math></span>, and the entries of its eigenvector with respect to <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>s</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>v</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> are not equal. Moreover, when considering adjusting the weights of edges, some necessary conditions for increasing <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> and decreasing <span><math><msub><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>(</mo><mi>G</mi><mo>)</mo></math></span> are also given respectively, both of which a","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129428"},"PeriodicalIF":3.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Aging in coevolving voter models","authors":"Byungjoon Min , Maxi San Miguel","doi":"10.1016/j.chaos.2025.116344","DOIUrl":"10.1016/j.chaos.2025.116344","url":null,"abstract":"<div><div>Aging, understood as the tendency to remain in a given state the longer the persistence time in that state, plays a crucial role in the dynamics of complex systems. In this paper, we explore the influence of aging on coevolution models, that is, models in which the dynamics of the states of the nodes in a complex network is coupled to the dynamics of the structure of the network. In particular we consider the coevolving voter model, and we introduce two versions of this model that include aging effects: the Link Aging Model (LAM) and the Node Aging Model (NAM). In the LAM, aging is associated with the persistence time of a link in the evolving network, while in the NAM, aging is associated with the persistence time of a node in a given state. We show that aging significantly affects the absorbing phase transition of the coevolution voter model, shifting the transition point in opposite directions for the LAM and NAM. We also show that the generic absorbing phase transition can disappear due to aging effects.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116344"},"PeriodicalIF":5.3,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Haowei Zhang , Yuexing Han , Gouhei Tanaka , Bing Wang
{"title":"Temporal correlation-based neural relational inference for binary dynamics","authors":"Haowei Zhang , Yuexing Han , Gouhei Tanaka , Bing Wang","doi":"10.1016/j.chaos.2025.116350","DOIUrl":"10.1016/j.chaos.2025.116350","url":null,"abstract":"<div><div>Binary-state dynamics are prevalent in nature, from societal dynamics to dynamical systems in physics. Reconstructing a network structure behind interacting binary-state dynamical systems is essential, as it can facilitate understanding of these dynamical systems and improve the accuracy of predicting dynamical behavior. So far, few works have focused on correlation information in binary-state temporal data to help reconstruct networks. In this study, we propose temporal correlation-based neural relational inference for binary dynamics (TCNRI), inspired by the maximum likelihood estimation of activation events in binary dynamics processes. TCNRI constructs instantaneous correlation features and long-term correlation features by analyzing activation events in the time series data. These features capture the correlation information and help TCNRI reconstruct the network structure. We treat the binary-state dynamical process as a Markov process and use neural networks to reproduce node dynamics based on the reconstructed network structure. We conduct simulations on the classic susceptible–infected–susceptible (SIS) dynamics and Ising dynamics. The results show that TCNRI significantly outperforms baseline models and can accurately reconstruct the network structure for both typical synthetic networks and real networks.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"196 ","pages":"Article 116350"},"PeriodicalIF":5.3,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143746963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Manuel A. Espinosa-García , Ahtziri González , Yesenia Villicaña-Molina
{"title":"The manifold of polygons degenerated to segments","authors":"Manuel A. Espinosa-García , Ahtziri González , Yesenia Villicaña-Molina","doi":"10.1016/j.difgeo.2025.102247","DOIUrl":"10.1016/j.difgeo.2025.102247","url":null,"abstract":"<div><div>In this paper we study the space <span><math><mi>L</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> of <em>n</em>-gons in the plane degenerated to segments. We prove that this space is a smooth real submanifold of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, and describe its topology in terms of the manifold <span><math><mi>M</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> of <em>n</em>-gons degenerated to segments and with the first vertex at 0. We show that <span><math><mi>M</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> and <span><math><mi>L</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> contain straight lines that form a basis of directions in each one of their tangent spaces, and we compute the geodesic equations in these manifolds. Finally, the quotient of <span><math><mi>L</mi><mo>(</mo><mi>n</mi><mo>)</mo></math></span> by the diagonal action of the affine complex group and the re-enumeration of the vertices is described.</div></div>","PeriodicalId":51010,"journal":{"name":"Differential Geometry and its Applications","volume":"99 ","pages":"Article 102247"},"PeriodicalIF":0.6,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Research problems from the 1st Chinese–Southeasteuropean conference on discrete mathematics and applications","authors":"Vedran Krčadinac , Shenggui Zhang , Liming Xiong , Dragan Stevanović","doi":"10.1016/j.dam.2025.02.037","DOIUrl":"10.1016/j.dam.2025.02.037","url":null,"abstract":"<div><div>This is a collection of open problems related to/presented at the 1st Chinese–Southeasteuropean conference on discrete mathematics and applications that was held at Serbian Academy of Sciences and Arts in Belgrade, Serbia, from June 9–14, 2024.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"371 ","pages":"Pages 99-104"},"PeriodicalIF":1.0,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143739099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Weak degeneracy of the square of K4-minor free graphs","authors":"Jing Ye , Jiani Zou , Miaomiao Han","doi":"10.1016/j.amc.2025.129439","DOIUrl":"10.1016/j.amc.2025.129439","url":null,"abstract":"<div><div>A graph <em>G</em> is called weakly <em>f</em>-degenerate with respect to a function <em>f</em> from <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> to the non-negative integers, if every vertex of <em>G</em> can be successively removed through a series of valid Delete and DeleteSave operations. The weak degeneracy <span><math><mi>w</mi><mi>d</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> is defined as the smallest integer <em>d</em> for which <em>G</em> is weakly <em>d</em>-degenerate, where <em>d</em> is a constant function. It was demonstrated that one plus the weak degeneracy can act as an upper bound for list-chromatic number and DP-chromatic number. Let <span><math><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>+</mo><mn>2</mn></math></span> if <span><math><mn>2</mn><mo>≤</mo><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≤</mo><mn>3</mn></math></span>, and <span><math><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mo>⌊</mo><mfrac><mrow><mn>3</mn><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⌋</mo></math></span> if <span><math><mi>Δ</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>≥</mo><mn>4</mn></math></span>. In this paper, we prove that for every <span><math><msub><mrow><mi>K</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-minor free graph <em>G</em>, <span><math><mi>w</mi><mi>d</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>≤</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span>, which implies that <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> is <span><math><mo>(</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-choosable and <span><math><mo>(</mo><mi>κ</mi><mo>(</mo><msup><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-DP-colorable. This work generalizes the result obtained by Lih et al. in [Discrete Mathematics, 269 (2003), 303-309] and Hetherington et al. in [Discrete Mathematics, 308 (2008), 4037-4043].</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"500 ","pages":"Article 129439"},"PeriodicalIF":3.5,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143738712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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